Question

Identify each pair of relationships among the groups in glucose (pink–blue, pink–dark blue, pink–black, blue–dark blue, blue-black, dark blue-black) as cis or trans.

Short answer

Pink-blue: Trans

Pink-dark blue: Trans

Pink-black: Trans

Blue-dark blue: Cis

Blue-black: Cis

Dark blue-black: Cis

Step-by-step solution

Chair form of cyclohexane 

There are four conformations possible for cyclohexane such as a chair, twist boat, boat, half chair. Among all the four conformations chair form of cyclohexane is considered a very stable one. Chair conformation of cyclohexane is as follow;

From the chair confirmation, we conclude that axial-equatorial bonds are always cis-trans. Axial-axial and equatorial-equatorial bonds are always cis to each other.

Relationship between -OH groups

Chair confirmation of glucose is as follow;

The pink color $-\mathrm{OH}$group is axial and the blue color $-\mathrm{OH}$group is equatorial so that they show a Trans relationship.

The pink color $-\mathrm{OH}$group is axial and the dark blue $-\mathrm{OH}$color is equatorial so that they show a Trans relationship.

The pink color $-\mathrm{OH}$group is axial and the black color $-\mathrm{OH}$is equatorial so that they show a Trans relationship.

The blue color $-\mathrm{OH}$group is equatorial and the dark blue color $-\mathrm{OH}$is also equatorial so that they show a cis relationship.

The blue color $-\mathrm{OH}$group is equatorial and the dark blue color $-\mathrm{OH}$is also equatorial so that they show a cis relationship.

The dark blue color $-\mathrm{OH}$group is equatorial and the black color$-\mathrm{OH}$ is also equatorial so that they show a cis relationship.